Transcript Applied Physics - Revision World

Applied Physics
Contents
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Rotational Dynamics
Thermodynamics & Engines
Rotational Dynamics
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Angular velocity: the angle of a circle (arc) mapped out by a
rotating object per second:
ω = θs-1
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Angular displacement: θ
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Angular velocity: ω = θt-1
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Angular acceleration: α = Δω/Δt
Rotational Dynamics
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Moment of Inertia: Inertia = objects have a degree of
reluctance to move. Moment of inertia is this but in rotational
movement. Objects oppose the movement of angular
acceleration. The more they oppose, the greater the moment of
inertia (kgm2)
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Circular disc:
I = Mr2/2
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Solid cylinder:
I = Mr2
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Solid sphere:
I = 2Mr2/5
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Kinetic Energy:
EK = ½Iω2
Rotational Dynamics
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Torque: Turning force
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Pulling force causes torque, T:
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In terms of inertia:
T = Iα
T = Fr
Rotational Momentum & Power
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Angular Momentum, (L): momentum = mass x velocity. Angular
momentum occurs in rotational movement
L (kgm2s-1) = Iω
angular momentum before = angular momentum after
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Impulse: change in momentum
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Angular Impulse, ΔL: change in angular momentum
ΔL = TΔt
(small torque for long duration = large torque for small duration)
Rotational Momentum & Power
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Work & Power:
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Work done = force x perpendicular distance… so…
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Work done = torque x angle rotated
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Power = force x speed… so…
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Power = torque x angular velocity
W = Tθ
P = Tω
1st Law of Thermodynamics
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1st Law of Thermodynamics: Energy can be neither created nor
destroyed (conservation of energy)
- Thus power generation processes and energy sources actually
involve conversion of energy from one form to another, rather
than creation of energy from nothing
ΔQ = ΔU + ΔW
ΔU: Change in internal energy of the system
ΔQ: Heat transferred into/out of the system
ΔW: Work done by/on the system
1st Law of Thermodynamics
Cylinder has area, A. A fluid is admitted at constant pressure, p
p = F/A
&
Wd = fd …
rearrange: F = pA

Wd = pAd (Ad = volume, V)
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 Wd = pV or ΔWd = pΔV
1st Law of Thermodynamics
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pV = nRT (Ideal Gas Law)
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Boyle’s Law: pV = constant
- Temperature remains constant (isothermal)
- pV = constant and p1V1 = p2V2
- ΔU = 0 because the internal energy is dependent on
temperature, which does not change
- ΔQ = ΔW. If the gas expands to do work ΔW, & amount of
heat ΔQ must be supplied
- compression or expansion produces the same graph
1st Law of Thermodynamics
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Adiabatic: no heat flow (ΔQ=0) into or out of a system
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For a change in pressure or volume in a system, the
temperature loss can be calculated:
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p1V1/T1 = p2V2/T2
At high p, low V: adiabatic = value
expected for isothermal at high T
At low p, high V: adiabatic cuts
isothermal at low T
Equation for adiabatic line:
pVγ = k
γ = Cp/Cv
k = constant
Adiabatic compression
1st Law of Thermodynamics
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Isovolumetric:
p 1 T1 = p 2 T 2
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Isobaric:
V1T1 = V2T2
Adiabatic compression
P-V diagrams & Engines
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Gases undergo changes that will eventually cause them to
return to the original state. An ideal gas undergoing these
changes has the properties shown below:
- Isovolumetric changes between a & b and c & d
- Isobaric changes between b & c and d & a
P-V diagrams & Engines
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Thermal Efficiency:
net work output ÷ heat input
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Actual efficiency of the engine will be lower than the value of
thermal efficiency alone, due to frictional losses within the
engine. The efficiency of a car = approx. 30%
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Petrol Engine: Otto Cycle
P-V diagrams & Engines
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Diesel Engine:
- Higher thermal efficiency that petrol engines
- Heavier than petrol engines
- More noise and incomplete combustion (pollution)
Both Engines:
power output: area of p-V loop x no cylinders x no cycles per sec
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maximum energy input: fuel calorific value x fuel flow rate
2nd Law & Engines
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2nd Law of Thermodynamics: Entropy of an isolated system not
in equilibrium will tend to increase over time, approaching a
maximum value at equilibrium
- i.e. entropy increases & all processes tend towards chaos
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Temperature gradient: Heat flows from a region of hot
temperature to a region of cold temperature
All heat engines give up their energy to a cold reservoir
Qin:heat flow from the hot reservoir to the engine
 Qout: heat flow from the engine to the cold reservoir.
 Work done by heat engine = Qin – Qout
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Efficiency = W/Qin = (Qin – Qout)/Qin
2nd Law & Engines
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1)
2)
3)
4)
5)
Limitations to Thermal Efficiency:
- in an engine:
TH cannot be too high  components could melt
TC will be in the range of atmospheric temperatures
Analysis of the engine cycle can help to improve efficiency
Design of ports so that gas can get enter & exit with min.
resistance
Lubrication reduces friction in bearings
Therefore an engine will never work at its theoretical efficiency
Summary
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Rotational Dynamics
Rotational Momentum & Power
1st Law of Thermodynamics
P-V diagrams & Engines
2nd Law & Engines